find-superquadric
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Implement the 6D Analytical Gradient
As of now, we make use of the expression of the analytical gradient in the context of a 4D problem (i.e., 3D for the location of the centroid, 1D for the rotation around the z-axis).
It might be beneficial to move toward a 6D problem formulation where we're required to express the complete analytical gradient by resorting e.g. to Vaskevicius2019^1.
Keeping the 4D and 6D analytical gradients separated and both available could be also advantageous.
year = {2016}, title = {{Revisiting Superquadric Fitting: A Numerically Stable Formulation}}, author = {Vaskevicius, Narunas and Birk, Andreas}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, issn = {0162-8828}, doi = {10.1109/tpami.2017.2779493}, pmid = {29990010}, pages = {220--233}, number = {1}, volume = {41}, keywords = {} }
It would be interesting to test recent software for automatic differentiation, like CppAD that is also linked in the Ipopt website, to evaluate the gradient.